The field of nanotechnology has rapidly evolved over the years as a result of significant interest in sub-micron research studies and applications. Accordingly, new challenges and technical problems have been encountered both at the research and application levels. These challenges span a wide range of fields of science and engineering. One such challenge is the ability to characterize surfaces and material properties at the sub-micron level. Several tools are available for this task. Such tools include the scanning electron microscope (SEM), the transmission electron microscope (TEM) and the scanning probe microscope (SPM), including the scanning tunneling microscope (STM) and the atomic force microscope (AFM). Each of these tools has its strengths and weaknesses. The AFM offers very high resolution (10 nm lateral and 0.05 nm vertical resolution are typical), compatibility with different types of samples and operating media, and generally requires no sample preparation. For these reasons, the AFM has become a widely used instrument in many disciplines. For example, in the field of semiconductors, AFM is used for surface roughness measurements of fabricated devices, integrated circuit failure analysis and nanolithography patterning resolution investigations.
Typically, a SPM such as an AFM includes a probe mounted on a cantilever, a sensor to measure the deflection of the cantilever and an actuator (sometimes referred to as a “scanner”) to provide three-dimensional relative motion between the probe and a sample. In contact mode, the probe is brought into contact with the sample at a user-specified force or cantilever deflection. The actuator is then moved in a raster fashion. During scanning, changes in the sample topography produce changes in the cantilever deflection. A controller maintains the deflection constant by adjusting the vertical displacement of the actuator (and, therefore, the cantilever-mounted probe) relative to the sample. The sample image is generated in response to the correcting voltage sent to the actuator.
The wide use of SPM and, in particular, AFM, in various fields has imposed ever-increasing stringent requirements on its performance. Among the factors limiting the tool's performance and repeatability is the accuracy of the actuator displacement. The accuracy of measurement data ultimately depends on the calibration of the actuator. Many actuators used in SPM, such as piezoelectric actuators, exhibit nonlinear input to displacement response. For example, piezoelectric actuators used in AFM have typical displacement ranges of 10 to 100 um laterally, and 4 to 10 um vertically. According to conventional calibration approaches, calibration of the actuator is performed by imaging a standard sample or grating having a known characteristic dimension. The voltage to displacement sensitivity is then computed from the applied voltage and the known dimension(s) of the standard. A linear sensitivity is assumed for vertical calibration.
Due to nonlinear actuator displacement, however, calibration may be affected by the bias voltage applied to the actuator to maintain probe-sample contact at the desired set-point during scanning. In addition, computed sensitivity may depend on scan speed due to creep (i.e., a slow response of the actuator to a rapid change in input signal). Thus, images obtained at a slow scan speed would yield larger sensitivity compared to images performed at faster speeds. Moreover, standards with a small height compared to the actuator range are commonly used for calibration to reduce the effect of hysteresis associated with the piezoelectric actuator. Consequently, calibration would only be accurate for a small fraction of the total actuator range (typically 3%). Imaging samples with features taller than the standard used for calibration could be corrupted by both hysteresis and nonlinearity due to the actuator's displacement.